Comparative Analysis of the 100-Year Return Level of the Average Monthly Rainfall for South Africa: Parent Distribution versus Extreme Value Distributions

Authors

Daniel Mashishi, Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga, 0727, South AfricaFollow
Daniel Maposa, Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga, 0727, South AfricaFollow
’Maseka Lesaoana, Department of Statistics and Operations Research, University of Limpopo, Private Bag X1106, Sovenga, 0727, South AfricaFollow

Author Country (or Countries)

South Africa

Abstract

In this paper, we model average monthly rainfall for South Africa using the parent distribution and extreme value theory (EVT). The 100-year return level plays an important role to hydrologists, meteorologists and civil engineers. Hence, the paper focuses on modelling the 100-year return level of average monthly rainfall for South Africa using the parent distribution and EVT. The present paper aims to compare the extreme quantile estimates of the EVT and parent distributions as well as to reveal the risk brought by heavy rainfall in South Africa. The method of maximum likelihood was used to estimate unknown parameters. We first investigate the parent distribution of the average monthly rainfall for South Africa. The results showed that the two-parameter Weibull distribution, which is in the domain of attraction of the Weibull family, is the appropriate parent distribution to model the data. We then perform a comparative analysis of the 100-year return level using the two-parameter Weibull distribution, the generalised extreme value distribution (GEVD), and the Poisson point process. The findings revealed that the 100-year return level of the two-parameter Weibull distribution was lower compared to that of the GEVD and Poisson point process model. The 100-year return level of the GEVD was equal to that of the observed maximum for the series, whereas that of the Poisson point process was slightly higher than the observed maximum average monthly rainfall for South Africa. Moreover, EVT models gave higher quantile estimation of the 100-year average monthly rainfall for South Africa compared to the parent distribution. Furthermore, EVT based estimation gave narrower confidence intervals as compared to the wider confidence interval of the parent distribution. Therefore, EVT models can play an important role in disaster risk reduction and civil engineering constructions, such as bridges and dams.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140507

Recommended Citation

Mashishi, Daniel; Maposa, Daniel; and Lesaoana, ’Maseka (2020) "Comparative Analysis of the 100-Year Return Level of the Average Monthly Rainfall for South Africa: Parent Distribution versus Extreme Value Distributions," Applied Mathematics & Information Sciences: Vol. 14: Iss. 5, Article 7.
DOI: http://dx.doi.org/10.18576/amis/140507
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss5/7